Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer. I. 15x2 + 26x + 8 = 0 II. 25y2 + 15y + 2 = 0

  1. x < y

  2. x > y

  3. x ≤ y

  4. x ≥ y

  5. x = y or no relation can be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 15x^2 + 26x + 8 = 0. Roots: (-26 +/- sqrt(676 - 480))/30 = (-26 +/- 14)/30. x = -40/30 = -4/3 or -12/30 = -0.4. II: 25y^2 + 15y + 2 = 0. Roots: (-15 +/- sqrt(225 - 200))/50 = (-15 +/- 5)/50. y = -20/50 = -0.4 or -10/50 = -0.2. Comparing: -1.33 <= -0.4 and -0.4 <= -0.2. Thus x <= y.

AI explanation

Applying the factorization method to the first equation, fifteen x squared plus twenty six x plus eight equals zero gives x equals negative two fifths and negative four thirds. For the second equation, twenty five y squared plus fifteen y plus two equals zero gives y equals negative one fifth and negative two fifths. Since the values of x are both less than or equal to negative two fifths, and the maximum value of x equals the minimum value of y while the other x value is smaller, x is less than or equal to y.

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